Question: Which of the following numbers is a factor of 112? ${3,5,8,12,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $112$ by each of our answer choices. $112 \div 3 = 37\text{ R }1$ $112 \div 5 = 22\text{ R }2$ $112 \div 8 = 14$ $112 \div 12 = 9\text{ R }4$ $112 \div 13 = 8\text{ R }8$ The only answer choice that divides into $112$ with no remainder is $8$ $ 14$ $8$ $112$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $112$ $112 = 2\times2\times2\times2\times7 8 = 2\times2\times2$ Therefore the only factor of $112$ out of our choices is $8$. We can say that $112$ is divisible by $8$.